Low-complexity robust tracking of high-order nonlinear systems with application to underactuated mechanical dynamics. (English) Zbl 1390.93275
Summary: This paper presents a low-complexity design approach with predefined transient and steady-state tracking performance for global practical tracking of uncertain high-order nonlinear systems. It is assumed that all nonlinearities and their bounding functions are unknown and the reference signal is time varying. A simple output tracking scheme consisting of nonlinearly transformed errors and positive design parameters is presented in the presence of virtual and actual control variables with high powers where the error transformation technique using time-varying performance functions is employed. Contrary to the existing results using known nonlinear bounding functions of model nonlinearities, the proposed tracking scheme can be implemented without using nonlinear bounding functions (i.e., the feedback domination design), any adaptive and function approximation techniques for estimating unknown nonlinearities. It is shown that the tracking performance of the proposed control system is ensured within preassigned bounds, regardless of high-power virtual and actual control variables. The motion tracking problem of an underactuated unstable mechanical system with unknown model parameters and nonlinearities is considered as a practical application, and simulation results are provided to show the effectiveness of the proposed theoretical result.
Keywords:
low-complexity tracking; high-order nonlinear systems; unknown nonlinearities; underactuated mechanical systemsReferences:
| [1] | Qian, CJ; Lin, W, A continuous feedback approach to global strong stabilization of nonlinear systems, IEEE Trans. Autom. Control, 46, 1061-1079, (2001) · Zbl 1012.93053 · doi:10.1109/9.935058 |
| [2] | Lin, W; Pongvuthithum, R, Nonsmooth adaptive stabilization of cascade systems with nonlinear parameterization via partial-state feedback, IEEE Trans. Autom. Control, 48, 1809-1816, (2003) · Zbl 1364.93711 · doi:10.1109/TAC.2003.817932 |
| [3] | Polendo, J; Qian, CJ, A generalized homogeneous domination approach for global stabilization of inherently nonlinear systems via output feedback, Int. J. Robust Nonlinear Control, 17, 605-629, (2007) · Zbl 1113.93087 · doi:10.1002/rnc.1139 |
| [4] | Li, WQ; Xie, XJ; Zhang, SY, Output-feedback stabilization of stochastic high-order nonlinear systems under weaker conditions, SIAM J. Control Optim., 49, 1262-1282, (2011) · Zbl 1228.93101 · doi:10.1137/100798259 |
| [5] | Fu, J; Ma, RC; Chai, TY, Global finite-time stabilization of a class of switched nonlinear systems with the powers of positive odd rational numbers, Automatica, 54, 360-373, (2015) · Zbl 1318.93081 · doi:10.1016/j.automatica.2015.02.023 |
| [6] | Sun, ZY; Li, T; Yang, SH, A unified time-varying feedback approach and its applications in adaptive stabilization of high-order uncertain nonlinear systems, Automatica, 70, 249-257, (2016) · Zbl 1339.93098 · doi:10.1016/j.automatica.2016.04.010 |
| [7] | Lin, W; Qian, CJ, Adaptive control of nonlinearly parameterized systems: the smooth feedback case, IEEE Trans. Autom. Control, 47, 1249-1266, (2002) · Zbl 1364.93399 · doi:10.1109/TAC.2002.800773 |
| [8] | Tian, J; Xie, XJ, Adaptive state-feedback stabilization for high-order stochastic nonlinear systems with uncertain control coefficients, Int. J. Control, 80, 1503-1516, (2007) · Zbl 1194.93213 · doi:10.1080/00207170701418917 |
| [9] | Xie, XJ; Tian, J, Adaptive state-feedback stabilization of high-order stochastic systems with nonlinear parameterization, Automatica, 45, 126-133, (2009) · Zbl 1154.93427 · doi:10.1016/j.automatica.2008.10.006 |
| [10] | Lv, LN; Sun, ZY; Xie, XJ, Adaptive control for high-order timedelay uncertain nonlinear system and application to chemical reactor system, Int. J. Adapt. Control Signal Process., 29, 224-241, (2015) · Zbl 1337.93047 · doi:10.1002/acs.2468 |
| [11] | Sun, ZY; Zhang, CH; Wang, Z, Adaptive disturbance attenuation for generailized high-order uncertain nonlinear systems, Automatica, 80, 102-109, (2017) · Zbl 1370.93101 · doi:10.1016/j.automatica.2017.02.036 |
| [12] | Lin, W; Qian, C, Robust regulation of a chain of power integrators perturbed by a lower-triangular vector field, Int. J. Robust Nonlinear Control, 10, 397-421, (2000) · Zbl 0962.93080 · doi:10.1002/(SICI)1099-1239(20000430)10:5<397::AID-RNC477>3.0.CO;2-N |
| [13] | Qian, C; Lin, W, Practical output tracking of nonlinear systems with uncontrollable unstable linearization, IEEE Trans. Autom. Control, 47, 21-36, (2002) · Zbl 1364.93349 · doi:10.1109/9.981720 |
| [14] | Zhao, X; Shi, P; Zheng, X; Zhang, J, Intelligent tracking control for a class of uncertain high-order nonlinear systems, IEEE Trans. Neural Netw. Learn. Syst., 27, 1976-1982, (2016) · doi:10.1109/TNNLS.2015.2460236 |
| [15] | Zhou, Q; Li, H; Wu, C; Wang, L; Ahn, CK, Adaptive fuzzy control of nonlinear systems with unmodeled dynamics and input saturation using small-gain approach, IEEE Trans. Syst. Man Cybern. Syst., 47, 1979-1989, (2017) · doi:10.1109/TSMC.2016.2586108 |
| [16] | Li, Y; Tong, S; Liu, L; Feng, G, Adaptive output-feedback control design with prescribed performance for switched nonlinear systems, Automatica, 80, 225-231, (2017) · Zbl 1370.93124 · doi:10.1016/j.automatica.2017.02.005 |
| [17] | Li, Y; Tong, S, Command-filtered-based fuzzy adaptive control design for MIMO switched nonstrict-feedback nonlinear systems, IEEE Trans. Fuzzy Syst., 25, 668-681, (2017) · doi:10.1109/TFUZZ.2016.2574913 |
| [18] | Tong, S; Li, Y; Sui, S, Adaptive fuzzy tracking control design for SISO uncertain nonstrict feedback nonlinear systems, IEEE Trans. Fuzzy Syst., 24, 1441-1454, (2016) · doi:10.1109/TFUZZ.2016.2540058 |
| [19] | Tong, S; Li, Y; Sui, S, Adaptive fuzzy output feedback control for switched nonstrict-feedback nonlinear systems with input nonlinearities, IEEE Trans. Fuzzy Syst., 24, 1426-1440, (2016) · doi:10.1109/TFUZZ.2016.2516587 |
| [20] | Bechlioulis, CP; Rovithakis, GA, A low-complexity global approximation-free control scheme with prescribed performance for unknown pure feedback systems, Automatica, 50, 1217-1226, (2014) · Zbl 1298.93171 · doi:10.1016/j.automatica.2014.02.020 |
| [21] | Theodorakopoulos, A; Rovithakis, GA, Guaranteeing preselected tracking quality for uncertain strict-feedback systems with deadzone input nonlinearity and disturbances via low-complexity control, Automatica, 54, 135-145, (2015) · Zbl 1318.93036 · doi:10.1016/j.automatica.2015.01.038 |
| [22] | Xie, XJ; Duan, N, Output tracking of high-order stochastic nonlinear systems with application to benchmark mechanical system, IEEE Trans. Autom. Control., 55, 1197-1202, (2010) · Zbl 1368.93229 · doi:10.1109/TAC.2010.2043004 |
| [23] | Krstic, M., Kanellakopoulos, I., Kokotovic, P.: Nonlinear and Adaptive Control Design. Wiley, Hoboken (1995) · Zbl 0763.93043 |
| [24] | Ge, SS; Wang, J, Robust adaptive neural control for a class of perturbed strict feedback nonlinear systems, IEEE Trans. Neural Netw., 13, 1409-1419, (2002) · doi:10.1109/TNN.2002.804306 |
| [25] | Li, P; Yang, GH, A novel adaptive control approach for nonlinear strict-feedback systems using nonlinearly parameterised fuzzy approximators, Int. J. Syst. Sci., 42, 517-527, (2011) · Zbl 1213.93101 · doi:10.1080/00207721003624576 |
| [26] | Ma, J; Zheng, Z; Li, P, Adaptive dynamic surface control of a class of nonlinear systems with unknown direction control gains and input saturation, IEEE Trans. Cybern., 45, 728-741, (2015) · doi:10.1109/TCYB.2014.2334695 |
| [27] | Wang, D; Huang, J, Neural network based adaptive dynamic surface control for nonlinear systems in strict-feedback form, IEEE Trans. Neural Netw., 16, 195-202, (2005) · doi:10.1109/TNN.2004.839354 |
| [28] | Wu, J; Li, J, Adaptive fuzzy control for perturbed strict-feedback nonlinear systems with predefiend tracking accuracy, Nonlinear Dyn., 83, 1185-1197, (2016) · Zbl 1351.93086 · doi:10.1007/s11071-015-2396-3 |
| [29] | Zhang, T; Ge, SS; Hang, CC, Adaptive neural network control for strict-feedback nonlinear systems using backstepping design, Automatica, 36, 1835-1846, (2000) · Zbl 0976.93046 · doi:10.1016/S0005-1098(00)00116-3 |
| [30] | Yip, PP; Hedrick, JK, Adaptive dynamic surface control: a simplified algorithm for adaptive backstepping control of nonlinear systems, Int. J. Control, 71, 959-979, (1998) · Zbl 0969.93037 · doi:10.1080/002071798221650 |
| [31] | Sontag, E.D.: Mathematical Control Theory. Springer, London (1998) · Zbl 0945.93001 · doi:10.1007/978-1-4612-0577-7 |
| [32] | Nussbaum, RD, Some remarks on a conjecture in parameter adaptive control, Syst. Control Lett., 3, 243-246, (1983) · Zbl 0524.93037 · doi:10.1016/0167-6911(83)90021-X |
| [33] | Ge, SS; Hong, F; Lee, TH, Adaptive neural control of nonlinear time-delay systems with unknown virtual control coefficients, IEEE Trans. Syst. Man Cybern. Part B Cybern., 34, 499-516, (2004) · doi:10.1109/TSMCB.2003.817055 |
| [34] | Rui, C., Reyhanoglu, M., Kolmanovsky, I., Cho, S., McClamroch, N.H.: Nonsmooth stabilization of an underactuated unstable two degrees of freedom mechanical system. In: Proceedings od 36th IEEE Conference on Decision Control, San Diego, CA, pp. 3998-4003 (1997) · Zbl 1318.93081 |
| [35] | Rehan, M; Jameel, A; Ahn, CK, Distributed consensus control of one-sided Lipschitz nonlinear multi-agent systems, IEEE Trans. Syst. Man Cybern. Syst., (2017) · doi:10.1109/TSMC.2017.2667701 |
| [36] | Agha, R; Rehan, M; Ahn, CK; Mustafa, G; Ahmad, S, Adaptive distributed consensus control of one-sided Lipschitz nonlinear multi-agents, IEEE Trans. Syst. Man Cybern. Syst., (2017) · doi:10.1109/TSMC.2017.2764521 |
| [37] | Wu, ZG; Shi, P; Su, H; Chu, J, Asynchronous \(l_{2}-l_{∞ }\) filtering for discrete-time stochastic Markov jump systems with randomly occurred sensor nonlinearities, Automatica, 50, 180-186, (2014) · Zbl 1417.93317 · doi:10.1016/j.automatica.2013.09.041 |
| [38] | Wu, ZG; Dong, S; Shi, P; Su, H; Huang, T; Lu, R, Fuzzy-model-based nonfragile guaranteed cost control of nonlinear Markov jump systems, IEEE Trans. Syst. Man Cybern. Syst., 47, 2388-2397, (2017) · doi:10.1109/TSMC.2017.2675943 |
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